Mathematical models of bipolar disorder

We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here

Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling

Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case $N>2$. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time-lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bi-stable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but non-symmetric and phase-shifted. For an intermediate range of time-lags inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.Comment: accepted by Phys.Rev.

New Analogues of Proline-Rich Protein Fragments. Synthesis and Their Effect on Resistance of Murine Thymocytes to Hydrocortisone

New analogues of proline-rich protein (PRP) fragment were synthesized by the solid phase method using Boc/Bzl procedure. Dimer of the nonapeptide as well as dimer, trimer and tetramer of hexapeptide fragments of PRP possessing immunotropic activity were obtained. Effect of the peptides on the resistance of murine thymocytes to hydrocortisone was the same as that of the reference compounds (hexapeptide and nonapeptide). Key words: PRP fragments analogues, solid phase peptide synthesis, immunotropic activity A proline-rich protein (PRP) was isolated by Janusz et al. from ovine colostrum The aim of the present paper was to obtain synthetic analogues of NP and HP, which could replace PRP isolated from colostrum and might show the same or even Biochem., 138, 9 (1984)]

Impact of dietary fat composition and quantity in pancreatic carcinogenesis: Recent advances and controversies.

A significant number of pancreatic cancer cases are due to modifiable risk factors, with many being attributed to increased body fatness. This has sparked investigators to examine the role played by high dietary fat intake in pancreatic cancer development and the mechanisms driving this connection. However, there is currently no consensus on how dietary fat quantity and composition specifically affect pancreatic carcinogenesis. The objective of this narrative review is to discuss the link between high total fat consumption and fatty acid composition (saturated, mono-, or poly-unsaturated fats) with pancreatic cancer incidence and progression. Following our detailed analysis of the strengths and weaknesses of recent preclinical and human studies, we discuss existing research gaps and opportunities, and provide recommendations for future studies. Numerous studies suggest that diets high in omega-3 polyunsaturated fatty acids are associated with reduced pancreatic cancer risk. However, the current evidence appears insufficient for a general conclusion regarding the impact of other types of fat in pancreatic carcinogenesis, with many studies providing inconclusive findings due to study limitations. Thus, we recommend future studies to include detailed methodology of the animal experiments, not limited to the diet composition, type of ingredients, formulations, and administration of the diets. Moreover, human studies should include a diverse population and well-characterized biomarkers for accurate determination of dietary fat intake. Ultimately, this will aid the study rigor, and improve our understanding of the impact of fat quantity and composition in pancreatic carcinogenesis

Impact of dietary fat composition and quantity in pancreatic carcinogenesis: Recent advances and controversies.

A significant number of pancreatic cancer cases are due to modifiable risk factors, with many being attributed to increased body fatness. This has sparked investigators to examine the role played by high dietary fat intake in pancreatic cancer development and the mechanisms driving this connection. However, there is currently no consensus on how dietary fat quantity and composition specifically affect pancreatic carcinogenesis. The objective of this narrative review is to discuss the link between high total fat consumption and fatty acid composition (saturated, mono-, or poly-unsaturated fats) with pancreatic cancer incidence and progression. Following our detailed analysis of the strengths and weaknesses of recent preclinical and human studies, we discuss existing research gaps and opportunities, and provide recommendations for future studies. Numerous studies suggest that diets high in omega-3 polyunsaturated fatty acids are associated with reduced pancreatic cancer risk. However, the current evidence appears insufficient for a general conclusion regarding the impact of other types of fat in pancreatic carcinogenesis, with many studies providing inconclusive findings due to study limitations. Thus, we recommend future studies to include detailed methodology of the animal experiments, not limited to the diet composition, type of ingredients, formulations, and administration of the diets. Moreover, human studies should include a diverse population and well-characterized biomarkers for accurate determination of dietary fat intake. Ultimately, this will aid the study rigor, and improve our understanding of the impact of fat quantity and composition in pancreatic carcinogenesis

Dynamics of Population Communities with Prey Migrations and Allee Effects: A Bifurcation Approach

The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives prey dispersal between patches, with the fragile prey populations, i.e. populations subject to the Allee effect. The resulting 3D and 4D non-linear systems depending on some parameters, which reflect \u27measures\u27 of factors under consideration, support rich dynamics and in particular a diverse number of predator-prey life history outcomes. The model\u27s mathematical analysis is carried out via submodels that focus in lower-dimensional settings. The outcomes depend on and, in fact, are quite sensitive to the structure of the system, the range of parameter values and initial conditions. We show that the system can support multistability and a diverse set of predator-prey life-history dynamics that include rather complex dynamical system outcomes. It is argued that, in general, evolution should favour heterogeneous settings including Allee effects, prey refuges and patch-specific predators